A stone is thrown vertically upward at an initial speed of 10m/s. Find the total time of the flight and the maximum height reached by the stone.

hf=hi+vi*t-4.8t^2

0=0+10*t-4.8t^2 solve for t.

Max height, solve for hf at time half the above time.

To find the total time of flight and the maximum height reached by the stone, we need to use the laws of motion and kinematic equations.

Step 1: Analyze the motion.
The stone is thrown vertically upward, so its initial velocity, u, is +10 m/s (positive because it's directed upward). The final velocity, v, will be zero at the maximum height reached. The acceleration due to gravity, g, is approximately 9.8 m/s² and acts downward.

Step 2: Find the time taken to reach the maximum height.
We can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is acceleration, and t is time.

Since the stone's final velocity at the maximum height is zero, we have:
0 = 10 - 9.8t
Solve this equation for t:
9.8t = 10
t = 10 / 9.8 ≈ 1.02 seconds

The stone takes approximately 1.02 seconds to reach the maximum height.

Step 3: Find the maximum height reached.
We can use the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is acceleration, and s is displacement.

Since the final velocity at the maximum height is zero, we have:
0² = 10² + 2(-9.8)s
0 = 100 - 19.6s
19.6s = 100
s = 100 / 19.6 ≈ 5.10 meters

The maximum height reached by the stone is approximately 5.10 meters.

In summary, the total time of flight is approximately 1.02 seconds, and the maximum height reached by the stone is approximately 5.10 meters.